75.111.2.129: More small copy changes

2014-11-17T06:23:40Z

More small copy changes

← Older revision		Revision as of 08:23, 17 November 2014
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	~~!bgcolor=#e7dcc3 colspan=2\|Truncated 8~~-~~simplex honeycomb~~
	\|-
	~~\|bgcolor=#ffffff align=center colspan=2\|(No image)~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|Type\|\|[[Uniform_8-polytope#Regular_and_uniform_honeycombs\|Uniform honeycomb]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Family\|\|[[Truncated simplectic honeycomb]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Schläfli symbol]]\|\|t<sub>~~0~~,1<~~/~~sub>{3<sup>[9]<~~/~~sup>}~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter–Dynkin diagram]]s\|\|{{CDD\|branch_11\|3ab\|nodes\|3ab\|nodes\|3ab\|nodes\|split2\|node}}~~
	\|-
	~~\|bgcolor=#e7dcc3\|8~~-~~face types\|\|[[8-simplex\|{3<sup>7<~~/~~sub>}~~]~~] [[File:8-simplex t0~~.~~svg\|30px]]~~, ~~[[Truncated 8-simplex\|~~t~~<sub>0~~,1</~~sub>{3<sup>7<~~/~~sub>}]] [[File:8-simplex t01~~.~~svg\|30px]]<BR>[[bitruncated 8-simplex\|t<sub>1,2<~~/~~sub>{3<sup>7<~~/~~sub>}~~]~~] [[File:8-simplex t12~~.~~svg\|30px]]~~, [~~[tritruncated 8-simplex\|t<sub>2,3<~~/~~sub>{3<sup>7<~~/~~sub>}]] [[File:8-simplex t23~~.~~svg\|30px]]<BR>[[Quadritruncated 8~~-~~simplex\|t<sub>3,4</sub>{3<sup>7</sub>}]] [[File:8~~-~~simplex t34.svg\|30px]]~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|Vertex figure\|\|Elongated [[7~~-~~simplex antiprism]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter notation\|Symmetry~~]~~]\|\|<math>{\tilde{A}}_8</math>×2~~, [<~~span/~~>[3<~~sup~~>~~[9]</sup>]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Properties\|\|[[vertex-transitive]]~~
	\|}
	~~In [[Eighth dimension\|eight-dimensional]] [[Euclidean geometry]]~~, the '''~~truncated 8-simplex honeycomb'''~~ is a ~~space-filling [[tessellation]] (~~or ~~[[honeycomb (geometry)\|honeycomb]])~~. The ~~tessellation fills space~~ by ~~[[8-simplex]]~~, ~~[[truncated 8-simplex]]~~, ~~[[bitruncated 8~~-~~simplex]]~~, ~~[[tritruncated 8-simplex]]~~, and ~~[[quadritruncated 8-simplex]] facets~~. ~~These facet types occur in proportions of 2~~:2:~~2:2:1 respectively~~ in the ~~whole honeycomb~~.

	~~It can~~ be ~~constructed by nine sets~~ of ~~parallel [[hyperplane]]~~s that ~~divide space~~. The ~~hyperplane intersections generate [[truncated 7-simplex honeycomb]] divisions~~ on ~~each hyperplane~~.

	~~== Related polytopes~~ and ~~honeycombs ==~~

	~~{{8-simplex honeycomb family}}~~

	~~==See also==~~
	~~Regular~~ and ~~uniform honeycombs~~ in ~~8-space:~~
	*[[8-cubic honeycomb]]
	*[[8-demicubic honeycomb]]
	*[[8-simplex honeycomb]]
	*[[Omnitruncated 8-simplex honeycomb]]
	*[[5_21 honeycomb\|5<~~sub~~>21<~~/sub~~> ~~honeycomb]]~~
	*[[2_51 honeycomb\|2<sub>51</sub> honeycomb]]
	*[[1_52 honeycomb\|1<sub>52</sub> honeycomb]]

	~~==Notes==~~
	~~{{reflist}}~~

	~~== References ==~~
	* [[Norman Johnson (mathematician)\|Norman Johnson]] ''Uniform Polytopes'', ~~Manuscript (1991)~~
	* '''Kaleidoscopes: Selected Writings of ~~H.S.M~~. ~~Coxeter'''~~, ~~edited by F. Arthur Sherk~~, ~~Peter McMullen, Anthony C~~. ~~Thompson~~, ~~Asia Ivic Weiss~~, ~~Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www~~.~~wiley~~.~~com/WileyCDA/WileyTitle/productCd-0471010030~~.~~html]~~
	** (Paper 22) H.S.M. ~~Coxeter~~, '~~'Regular and Semi Regular Polytopes I''~~, ~~[Math~~. ~~Zeit. 46 (1940) 380-407, MR 2~~,10~~] (1~~.~~9 Uniform space-fillings)~~
	** (Paper 24) H.S.~~M. Coxeter~~, ~~''Regular~~ and ~~Semi-Regular Polytopes III''~~, ~~[Math~~. ~~Zeit. 200 (1988) 3-45]~~
	~~{{Honeycombs}}~~

	~~[[Category:Honeycombs (geometry)]]~~
	~~[[Category:9-polytopes]]~~

en>Duoduoduo: /* Relevant contexts */ notation

2013-08-14T16:25:29Z

Relevant contexts: notation

New page

{| class="wikitable" align="right" style="margin-left:10px" width="320"
!bgcolor=#e7dcc3 colspan=2|Truncated 8-simplex honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|(No image)
|-
|bgcolor=#e7dcc3|Type||[[Uniform_8-polytope#Regular_and_uniform_honeycombs|Uniform honeycomb]]
|-
|bgcolor=#e7dcc3|Family||[[Truncated simplectic honeycomb]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]||t0,1{3[9]}
|-
|bgcolor=#e7dcc3|[[Coxeter–Dynkin diagram]]s||{{CDD|branch_11|3ab|nodes|3ab|nodes|3ab|nodes|split2|node}}
|-
|bgcolor=#e7dcc3|8-face types||[[8-simplex|{37}]] [[File:8-simplex t0.svg|30px]], [[Truncated 8-simplex|t0,1{37}]] [[File:8-simplex t01.svg|30px]] [[bitruncated 8-simplex|t1,2{37}]] [[File:8-simplex t12.svg|30px]], [[tritruncated 8-simplex|t2,3{37}]] [[File:8-simplex t23.svg|30px]] [[Quadritruncated 8-simplex|t3,4{37}]] [[File:8-simplex t34.svg|30px]]
|-
|bgcolor=#e7dcc3|Vertex figure||Elongated [[7-simplex antiprism]]
|-
|bgcolor=#e7dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_8</math>×2, [[3[9]]]
|-
|bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
|}
In [[Eighth dimension|eight-dimensional]] [[Euclidean geometry]], the '''truncated 8-simplex honeycomb''' is a space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). The tessellation fills space by [[8-simplex]], [[truncated 8-simplex]], [[bitruncated 8-simplex]], [[tritruncated 8-simplex]], and [[quadritruncated 8-simplex]] facets. These facet types occur in proportions of 2:2:2:2:1 respectively in the whole honeycomb.

It can be constructed by nine sets of parallel [[hyperplane]]s that divide space. The hyperplane intersections generate [[truncated 7-simplex honeycomb]] divisions on each hyperplane.

== Related polytopes and honeycombs ==

{{8-simplex honeycomb family}}

==See also==
Regular and uniform honeycombs in 8-space:
*[[8-cubic honeycomb]]
*[[8-demicubic honeycomb]]
*[[8-simplex honeycomb]]
*[[Omnitruncated 8-simplex honeycomb]]
*[[5_21 honeycomb|521 honeycomb]]
*[[2_51 honeycomb|251 honeycomb]]
*[[1_52 honeycomb|152 honeycomb]]

==Notes==
{{reflist}}

== References ==
* [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
{{Honeycombs}}

[[Category:Honeycombs (geometry)]]
[[Category:9-polytopes]]

Discrete time and continuous time - Revision history

75.111.2.129: More small copy changes

en>Duoduoduo: /* Relevant contexts */ notation